Expressions for 'c' and 'd' in terms of 'a' will be [tex](d=4a)[/tex] and [tex](c=a^2+8)[/tex].
In question number 12, it's given that [tex](a+\sqrt{8})^2[/tex] can be written as [tex](c+d\sqrt{2})[/tex].
So the expression representing the situation will be,
[tex](a+\sqrt{8})^2=(c+d\sqrt{2})[/tex]
Now simplify the expression,
[tex]a^2+8+2a\sqrt{8}=c+d\sqrt{2}[/tex]
[tex](a^2+8)+2a\sqrt{8}=(c+d\sqrt{2})[/tex]
[tex](a^2+8)+4a\sqrt{2}=(c+d\sqrt{2})[/tex]
Compare both the sides of the equation,
[tex]c=a^2+8[/tex]
[tex]4a\sqrt{2}=d\sqrt{2}[/tex]
[tex]d=4a[/tex]
Therefore, [tex](d=4a)[/tex] and [tex](c=a^2+8)[/tex] will be the expressions for c and d in terms of a.
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https://brainly.com/question/13030227
